Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4598061 | Journal of Pure and Applied Algebra | 2008 | 9 Pages |
Abstract
This paper concerns preprojective representations of a finite connected valued quiver without oriented cycles. For each such representation, an explicit formula in terms of the geometry of the quiver gives a unique, up to a certain equivalence, shortest (+)-admissible sequence such that the corresponding composition of reflection functors annihilates the representation. The set of equivalence classes of the above sequences is a partially ordered set that contains a great deal of information about the preprojective component of the Auslander–Reiten quiver. The results apply to the study of reduced words in the Weyl group associated with an indecomposable symmetrizable generalized Cartan matrix.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Mark Kleiner, Helene R. Tyler,